ψ(x) is the four-component wave function of the Dirac equation，that is ψ(x) can be expressed by a column vector (ψ1(x) ψ2(x) ψ3(x) ψ4(x)） ,under a lorentz transformation,it will become ψ'(x').I am confused that how ψ'(x') can be expressd(adsbygoogle = window.adsbygoogle || []).push({});

in the form which is stated by textbooks: ψ'(x')=S(a)ψ(x)

（a is the matrix of the lorentz transformation ,S(a) is a 4*4 matrix which is a function of the parameters of a ）

clearly.ψ'(x') is a funtion of x',ψ(x) is funtion of x,my question is for example ,how can

ψ'1(x') can be expressed by a linear combination of ψ1(x), ψ2(x) ,ψ3(x)and ψ4(x)?

is there someone can help me?

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# Question about lorentz-covariance of Dirac equation

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